From the formula, \(\mu = np = 40000 \cdot \frac{1}{4} = 10000\text{.}\) So, using Poisson’s probability function
\begin{equation*}
f_{\text{Poisson}} = \frac{10000^{x}}{x!}e^{-10000}
\end{equation*}
would require you to compute
\begin{equation*}
e^{-10000} \sum_{x=10000}^{\infty} \frac{10000^{x}}{x!}
\end{equation*}
which is also a mess. However with a computational resource such as a graphing calculator, just compare 1 - binomcdf(40000,0.25,9999) to 1-poissoncdf(10000,9999) noting that the complement of the given question is from X from 0 to 9999. The two values should be relatively close